What is Boltzmann's constant?

$A$ fixed amount of gas has a volume $V$ at constant pressure. If the temperature of the gas is increased such that the $v_{rms}$ of the molecules doubles,then its new volume will be .......

The temperature of an open room of volume $30\ m^3$ increases from $17^\circ C$ to $27^\circ C$ due to sunshine. The atmospheric pressure in the room remains $1 \times 10^5\ Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating,then $n_f - n_i$ will be:

$A$ container holds $6 \ g$ of oxygen at a pressure $P$ and temperature $400 \ K$. $A$ small hole is made in the container so that oxygen can leak out. How much oxygen (in $g$) will leak out by the time the pressure becomes $P/2$ and the temperature becomes $300 \ K$?

One litre of Helium gas at a pressure $76 \ cm$ of $Hg$ and temperature ${27}^\circ C$ is heated until its pressure and volume are doubled. The final temperature attained by the gas is ..... $^\circ C$

The $PV$ versus $T$ graph for equal masses of $H_2$,$He$,and $O_2$ is shown in the figure. Choose the correct alternative.